Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT
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| Format: | Preprint |
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2020
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| _version_ | 1866915133262921728 |
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| author | Carlier, Guillaume Eichinger, Katharina Kroshnin, Alexey |
| author_facet | Carlier, Guillaume Eichinger, Katharina Kroshnin, Alexey |
| contents | In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced by Bigot, Cazelles and Papadakis (2019) as a regularization of Wasserstein barycenters first presented by Agueh and Carlier (2011). After characterizing these barycenters in terms of a system of Monge-Ampère equations, we prove some global moment and Sobolev bounds as well as higher regularity properties. We finally establish a central limit theorem for entropic-Wasserstein barycenters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_10701 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT Carlier, Guillaume Eichinger, Katharina Kroshnin, Alexey Analysis of PDEs Probability 49Q25, 35J96, 60B12 In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced by Bigot, Cazelles and Papadakis (2019) as a regularization of Wasserstein barycenters first presented by Agueh and Carlier (2011). After characterizing these barycenters in terms of a system of Monge-Ampère equations, we prove some global moment and Sobolev bounds as well as higher regularity properties. We finally establish a central limit theorem for entropic-Wasserstein barycenters. |
| title | Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT |
| topic | Analysis of PDEs Probability 49Q25, 35J96, 60B12 |
| url | https://arxiv.org/abs/2012.10701 |